--- /dev/null
+/*
+ * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/*
+ * This file contains the core "big integer" functions for the i15
+ * implementation, that represents integers as sequences of 15-bit
+ * words.
+ */
+
+/* see inner.h */
+uint32_t
+br_i15_iszero(const uint16_t *x)
+{
+ uint32_t z;
+ size_t u;
+
+ z = 0;
+ for (u = (x[0] + 15) >> 4; u > 0; u --) {
+ z |= x[u];
+ }
+ return ~(z | -z) >> 31;
+}
+
+/* see inner.h */
+uint16_t
+br_i15_ninv15(uint16_t x)
+{
+ uint32_t y;
+
+ y = 2 - x;
+ y = MUL15(y, 2 - MUL15(x, y));
+ y = MUL15(y, 2 - MUL15(x, y));
+ y = MUL15(y, 2 - MUL15(x, y));
+ return MUX(x & 1, -y, 0) & 0x7FFF;
+}
+
+/* see inner.h */
+uint32_t
+br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl)
+{
+ uint32_t cc;
+ size_t u, m;
+
+ cc = 0;
+ m = (a[0] + 31) >> 4;
+ for (u = 1; u < m; u ++) {
+ uint32_t aw, bw, naw;
+
+ aw = a[u];
+ bw = b[u];
+ naw = aw + bw + cc;
+ cc = naw >> 15;
+ a[u] = MUX(ctl, naw & 0x7FFF, aw);
+ }
+ return cc;
+}
+
+/* see inner.h */
+uint32_t
+br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl)
+{
+ uint32_t cc;
+ size_t u, m;
+
+ cc = 0;
+ m = (a[0] + 31) >> 4;
+ for (u = 1; u < m; u ++) {
+ uint32_t aw, bw, naw;
+
+ aw = a[u];
+ bw = b[u];
+ naw = aw - bw - cc;
+ cc = naw >> 31;
+ a[u] = MUX(ctl, naw & 0x7FFF, aw);
+ }
+ return cc;
+}
+
+/*
+ * Constant-time division. The divisor must not be larger than 16 bits,
+ * and the quotient must fit on 17 bits.
+ */
+static uint32_t
+divrem16(uint32_t x, uint32_t d, uint32_t *r)
+{
+ int i;
+ uint32_t q;
+
+ q = 0;
+ d <<= 16;
+ for (i = 16; i >= 0; i --) {
+ uint32_t ctl;
+
+ ctl = LE(d, x);
+ q |= ctl << i;
+ x -= (-ctl) & d;
+ d >>= 1;
+ }
+ if (r != NULL) {
+ *r = x;
+ }
+ return q;
+}
+
+/* see inner.h */
+void
+br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
+{
+ /*
+ * Constant-time: we accept to leak the exact bit length of the
+ * modulus m.
+ */
+ unsigned m_bitlen, mblr;
+ size_t u, mlen;
+ uint32_t hi, a0, a, b, q;
+ uint32_t cc, tb, over, under;
+
+ /*
+ * Simple case: the modulus fits on one word.
+ */
+ m_bitlen = m[0];
+ if (m_bitlen == 0) {
+ return;
+ }
+ if (m_bitlen <= 15) {
+ uint32_t rem;
+
+ divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
+ x[1] = rem;
+ return;
+ }
+ mlen = (m_bitlen + 15) >> 4;
+ mblr = m_bitlen & 15;
+
+ /*
+ * Principle: we estimate the quotient (x*2^15+z)/m by
+ * doing a 30/15 division with the high words.
+ *
+ * Let:
+ * w = 2^15
+ * a = (w*a0 + a1) * w^N + a2
+ * b = b0 * w^N + b2
+ * such that:
+ * 0 <= a0 < w
+ * 0 <= a1 < w
+ * 0 <= a2 < w^N
+ * w/2 <= b0 < w
+ * 0 <= b2 < w^N
+ * a < w*b
+ * I.e. the two top words of a are a0:a1, the top word of b is
+ * b0, we ensured that b0 is "full" (high bit set), and a is
+ * such that the quotient q = a/b fits on one word (0 <= q < w).
+ *
+ * If a = b*q + r (with 0 <= r < q), then we can estimate q by
+ * using a division on the top words:
+ * a0*w + a1 = b0*u + v (with 0 <= v < b0)
+ * Then the following holds:
+ * 0 <= u <= w
+ * u-2 <= q <= u
+ */
+ hi = x[mlen];
+ if (mblr == 0) {
+ a0 = x[mlen];
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) + x[mlen];
+ b = m[mlen];
+ } else {
+ a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) | (((x[mlen] << (15 - mblr))
+ | (x[mlen - 1] >> mblr)) & 0x7FFF);
+ b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
+ }
+ q = divrem16(a, b, NULL);
+
+ /*
+ * We computed an estimate for q, but the real one may be q,
+ * q-1 or q-2; moreover, the division may have returned a value
+ * 8000 or even 8001 if the two high words were identical, and
+ * we want to avoid values beyond 7FFF. We thus adjust q so
+ * that the "true" multiplier will be q+1, q or q-1, and q is
+ * in the 0000..7FFF range.
+ */
+ q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
+
+ /*
+ * We subtract q*m from x (x has an extra high word of value 'hi').
+ * Since q may be off by 1 (in either direction), we may have to
+ * add or subtract m afterwards.
+ *
+ * The 'tb' flag will be true (1) at the end of the loop if the
+ * result is greater than or equal to the modulus (not counting
+ * 'hi' or the carry).
+ */
+ cc = 0;
+ tb = 1;
+ for (u = 1; u <= mlen; u ++) {
+ uint32_t mw, zl, xw, nxw;
+
+ mw = m[u];
+ zl = MUL15(mw, q) + cc;
+ cc = zl >> 15;
+ zl &= 0x7FFF;
+ xw = x[u];
+ nxw = xw - zl;
+ cc += nxw >> 31;
+ nxw &= 0x7FFF;
+ x[u] = nxw;
+ tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
+ }
+
+ /*
+ * If we underestimated q, then either cc < hi (one extra bit
+ * beyond the top array word), or cc == hi and tb is true (no
+ * extra bit, but the result is not lower than the modulus).
+ *
+ * If we overestimated q, then cc > hi.
+ */
+ over = GT(cc, hi);
+ under = ~over & (tb | LT(cc, hi));
+ br_i15_add(x, m, over);
+ br_i15_sub(x, m, under);
+}
+
+/* see inner.h */
+void
+br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
+ const uint16_t *m, uint16_t m0i)
+{
+ size_t len, len4, u, v;
+ uint32_t dh;
+
+ len = (m[0] + 15) >> 4;
+ len4 = len & ~(size_t)3;
+ br_i15_zero(d, m[0]);
+ dh = 0;
+ for (u = 0; u < len; u ++) {
+ uint32_t f, xu, r, zh;
+
+ xu = x[u + 1];
+ f = MUL15(d[1] + MUL15(x[u + 1], y[1]), m0i) & 0x7FFF;
+
+ r = 0;
+ for (v = 0; v < len4; v += 4) {
+ uint32_t z;
+
+ z = d[v + 1] + MUL15(xu, y[v + 1])
+ + MUL15(f, m[v + 1]) + r;
+ r = z >> 15;
+ d[v + 0] = z & 0x7FFF;
+ z = d[v + 2] + MUL15(xu, y[v + 2])
+ + MUL15(f, m[v + 2]) + r;
+ r = z >> 15;
+ d[v + 1] = z & 0x7FFF;
+ z = d[v + 3] + MUL15(xu, y[v + 3])
+ + MUL15(f, m[v + 3]) + r;
+ r = z >> 15;
+ d[v + 2] = z & 0x7FFF;
+ z = d[v + 4] + MUL15(xu, y[v + 4])
+ + MUL15(f, m[v + 4]) + r;
+ r = z >> 15;
+ d[v + 3] = z & 0x7FFF;
+ }
+ for (; v < len; v ++) {
+ uint32_t z;
+
+ z = d[v + 1] + MUL15(xu, y[v + 1])
+ + MUL15(f, m[v + 1]) + r;
+ r = z >> 15;
+ d[v + 0] = z & 0x7FFF;
+ }
+
+ zh = dh + r;
+ d[len] = zh & 0x7FFF;
+ dh = zh >> 31;
+ }
+
+ /*
+ * Restore the bit length (it was overwritten in the loop above).
+ */
+ d[0] = m[0];
+
+ /*
+ * d[] may be greater than m[], but it is still lower than twice
+ * the modulus.
+ */
+ br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0)));
+}
+
+/* see inner.h */
+void
+br_i15_to_monty(uint16_t *x, const uint16_t *m)
+{
+ unsigned k;
+
+ for (k = (m[0] + 15) >> 4; k > 0; k --) {
+ br_i15_muladd_small(x, 0, m);
+ }
+}
+
+/* see inner.h */
+void
+br_i15_modpow(uint16_t *x,
+ const unsigned char *e, size_t elen,
+ const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2)
+{
+ size_t mlen;
+ unsigned k;
+
+ mlen = ((m[0] + 31) >> 4) * sizeof m[0];
+ memcpy(t1, x, mlen);
+ br_i15_to_monty(t1, m);
+ br_i15_zero(x, m[0]);
+ x[1] = 1;
+ for (k = 0; k < ((unsigned)elen << 3); k ++) {
+ uint32_t ctl;
+
+ ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1;
+ br_i15_montymul(t2, x, t1, m, m0i);
+ CCOPY(ctl, x, t2, mlen);
+ br_i15_montymul(t2, t1, t1, m, m0i);
+ memcpy(t1, t2, mlen);
+ }
+}
+
+/* see inner.h */
+void
+br_i15_encode(void *dst, size_t len, const uint16_t *x)
+{
+ unsigned char *buf;
+ size_t u, xlen;
+ uint32_t acc;
+ int acc_len;
+
+ xlen = (x[0] + 15) >> 4;
+ if (xlen == 0) {
+ memset(dst, 0, len);
+ return;
+ }
+ u = 1;
+ acc = 0;
+ acc_len = 0;
+ buf = dst;
+ while (len -- > 0) {
+ if (acc_len < 8) {
+ if (u <= xlen) {
+ acc += (uint32_t)x[u ++] << acc_len;
+ }
+ acc_len += 15;
+ }
+ buf[len] = (unsigned char)acc;
+ acc >>= 8;
+ acc_len -= 8;
+ }
+}
+
+/* see inner.h */
+uint32_t
+br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m)
+{
+ /*
+ * Two-pass algorithm: in the first pass, we determine whether the
+ * value fits; in the second pass, we do the actual write.
+ *
+ * During the first pass, 'r' contains the comparison result so
+ * far:
+ * 0x00000000 value is equal to the modulus
+ * 0x00000001 value is greater than the modulus
+ * 0xFFFFFFFF value is lower than the modulus
+ *
+ * Since we iterate starting with the least significant bytes (at
+ * the end of src[]), each new comparison overrides the previous
+ * except when the comparison yields 0 (equal).
+ *
+ * During the second pass, 'r' is either 0xFFFFFFFF (value fits)
+ * or 0x00000000 (value does not fit).
+ *
+ * We must iterate over all bytes of the source, _and_ possibly
+ * some extra virutal bytes (with value 0) so as to cover the
+ * complete modulus as well. We also add 4 such extra bytes beyond
+ * the modulus length because it then guarantees that no accumulated
+ * partial word remains to be processed.
+ */
+ const unsigned char *buf;
+ size_t mlen, tlen;
+ int pass;
+ uint32_t r;
+
+ buf = src;
+ mlen = (m[0] + 15) >> 4;
+ tlen = (mlen << 1);
+ if (tlen < len) {
+ tlen = len;
+ }
+ tlen += 4;
+ r = 0;
+ for (pass = 0; pass < 2; pass ++) {
+ size_t u, v;
+ uint32_t acc;
+ int acc_len;
+
+ v = 1;
+ acc = 0;
+ acc_len = 0;
+ for (u = 0; u < tlen; u ++) {
+ uint32_t b;
+
+ if (u < len) {
+ b = buf[len - 1 - u];
+ } else {
+ b = 0;
+ }
+ acc |= (b << acc_len);
+ acc_len += 8;
+ if (acc_len >= 15) {
+ uint32_t xw;
+
+ xw = acc & (uint32_t)0x7FFF;
+ acc_len -= 15;
+ acc = b >> (8 - acc_len);
+ if (v <= mlen) {
+ if (pass) {
+ x[v] = r & xw;
+ } else {
+ uint32_t cc;
+
+ cc = (uint32_t)CMP(xw, m[v]);
+ r = MUX(EQ(cc, 0), r, cc);
+ }
+ } else {
+ if (!pass) {
+ r = MUX(EQ(xw, 0), r, 1);
+ }
+ }
+ v ++;
+ }
+ }
+
+ /*
+ * When we reach this point at the end of the first pass:
+ * r is either 0, 1 or -1; we want to set r to 0 if it
+ * is equal to 0 or 1, and leave it to -1 otherwise.
+ *
+ * When we reach this point at the end of the second pass:
+ * r is either 0 or -1; we want to leave that value
+ * untouched. This is a subcase of the previous.
+ */
+ r >>= 1;
+ r |= (r << 1);
+ }
+
+ x[0] = m[0];
+ return r & (uint32_t)1;
+}
projects / BearSSL / blobdiff